The present invention relates to a method of stabilizing a model vector, which is a map of a vectorial physical quantity of a machine and is formed in a computing circuit containing at least one integrator, by integration of a sum vector formed by an input vector and a correction vector. The invention relates further to the application of this method as well as to apparatus for achieving this purpose.
The problem underlying the invention is the influence of integration errors of technical integrators for determining parameters which are required as mathematical images of physical quantities with integral relationships in the control of technical processes.
In a preferred field of application of the invention, a rotating field machine is controlled or regulated highly dynamically by the provision that its stator current is preset by a converter as a function of two flux direction related control quantities which influence the stator current component parallel to the flux and perpendicular to the flux independently. In order to change from the flux direction related control quantities to the so-called "stator-related" control quantities of the converter which are stationary in space, information on the direction of the flux vector is required and, if control of the flux is of advantage, also the absolute magnitude of the flux vector must be determined.
In German Pat. No. 18 06 769, (U.S. Pat. No. 3,593,083) a so-called "voltage model" is proposed for this purpose which, according to the relationships EQU e.sub.s =u.sub.s -r.sup.s .multidot.i.sub.s -l.sup..sigma. di.sub.s /dt EQU .psi..sub.s =.intg.e.sub.s dt
calculates from the stator voltage vector u.sub.s and the stator current vector i.sub.s the orthogonal components (subscript s1 and s2) from corresponding measured voltage and current values as well as from parameters for the stator resistance r.sup.s and the leakage inductance l.sup..sigma., the EMF vector e and by means of integrators for integration by components, the corresponding flux vector .psi..sub.s in the orthogonal stator-related coordinates. Since, however, integrators exhibit null-drift and other integration errors, the model vector .psi..sub.s calculated in this computing circuit as the model flux is different from the mathematical integral of the input vector e.sub.s. The determined flux vector .psi..sub.s is therefore only an imperfect image (map) of the actual flux.
In FIG. 1 the model vector .psi..sub.s is shown in relation to the Cartesian coordinate axes S1 and S2 fixed in space. In this coordinate presentation it has the components .psi..sub.s1 and .psi..sub.s2 shown in FIG. 1 which, according to .psi..sub.sz =.psi. cos .phi..sub.s and .psi..sub.s2 =.psi. sin .phi..sub.s are mathematically equivalent to the polar amplitude coordinate .psi. (model vector magnitude) and to the polar angle coordinate .phi..sub.s (direction of the model vector in the S1, S2 system.
For the processing of the angle coordinate, a presentation by a pair of trigonometric functions (cos .phi..sub.s, sin .phi..sub.s) is frequently of advantage which describes the Cartesian components of a unit vector .phi..sub.s given by the angle .phi..sub.s. So-called "vector analyzers" furnish the magnitude and the pair of trigonometric functions from the vector components. Rotation of the vector .psi. by an angle .epsilon. corresponds to a rotation of the coordinate system and can be carried out by an angle addition in a so-called "vector rotator" to which the angle of rotation is fed as a corresponding unit vector .epsilon.=(cos .epsilon., sin .epsilon.). The angle coordinate of the vector in the rotated coordinate system corresponds to a new unit vector (.phi..sub.s +.epsilon.) from which follow by component-wise multiplication of the unchanged magnitude .psi., the corresponding Cartesian vector components in the rotated system, or the components of the rotated vector in the original system.
FIG. 1 now shows the case that, in the coordinate system fixed in space, the vectorial physical quantity .psi..sub.s while it revolves uniformly and therefore would have to be imaged mathematically by the components .psi..multidot.cos wt and .psi..multidot.sin wt (this corresponds to a concentric circle about the coordinate origin Oo), the drift of technical integrators leads to the condition that the locus of the model vector .psi..sub.s furnished by the integrators takes an eccentric course. As "eccentricity" or "d-c component vector" of the locus is designated here the vector .DELTA. leading from Oo to the center O of the locus. The latter has the stator-oriented Cartesian coordinates .DELTA..sub.s1 and .DELTA..sub.s2. The Cartesian components .psi..sub.s1 and .psi..sub.s2 of the model vector are therefore obtained as .psi..sub.s1 =.DELTA..sub.s1 +.psi. cos wt, .psi..sub.s2 =.DELTA..sub.s2 +.psi. sin wt with the d-c components .DELTA..sub.s1 and .DELTA..sub.s2.
In order to suppress the d-c components, it is provided in the mentioned German Pat. No. 18 06 769 to bring the model vector .psi..sub.s of the flux via a null regulator which forms a correction vector therefrom. The vectorial sum (sum vector) of the negative correction vector and the predetermined vector e.sub.s of the EMF is then subjected to the integration for forming the vector .psi..sub.s itself.
The control loop formed thereby thus controls the d-c components in the integrator output to zero but causes an angle error which leads dynamically and statically to a misadjustment of the model vector and becomes larger and larger at lower frequencies. Therefore, this d-c component control can intervene only relatively weakly and cannot level out larger errors. Therefore, a so-called "adaptive voltage model" is proposed in German Offenlegungsschrift No. 28 33 542 (U.S. Pat. No. 4,282,473), in which the feedback loop is conducted via a P-controller and an I-controller, the action of which is weighted as a function of frequency. Thereby a frequency-independent angle error is obtained which can be taken into consideration in the design of the controller as long as it can be kept relatively small. However, angle errors of up to 40.degree. are required for sufficient stability of the locus, and their compensation in the controller leads to difficulties.
It is therefore provided in German Offenlegungsschrift No. 30 26 202 (U.S. Pat. No. 4,388,577) not to level the model vector to zero in the feedback loop, but to a reference value which is obtained in other ways. Other possibilities for calculating the flux from suitable actual values are available. In particular, a computing circuit known as a "current model" can be used which calculates from the stator current the rotor position (or also the rotor frequency), as well, in the case of synchronous machines, from the field current, calculates the flux generated in the machine by the current by simulating the dynamic processes of the machine.
This current model is of advantage particularly if, at low speeds, the EMF has only small amplitudes and therefore, the calculation of the flux in the voltage model is subjected to computing errors. In this known arrangement, however, the model vector calculated by the current model is used as the reference value for the null regulator in the feedback loop of the voltage model and the action of the null regulators is frequency-dependent to such a degree that this null regulation is effective practically only at low frequencies. It follows from this that at low frequencies, the voltage model is controlled by the current model. Then, the current model largely determines the model vector of the voltage model, and the influence of the voltage model is preponderant only at higher frequencies. While this procedure makes possible the determination of the flux vector in a large frequency region without the need to switch between the current model and the voltage model, the result of the voltage model depends on the quality of the current model. In addition, it presupposes the existence of the current model. The same applies also if the voltage model were controlled by the reference voltage preset for the control of the flux. In this connection, it has also been proposed already to recalculate the model vector furnished by the voltage model as well as the vector furnished by the current model as the reference value into polar coordinates in order to determine the correction vector formed by appropriate controls in polar coordinates and to impress it on the input vector e.sub.s.